Method for inducing agglomeration of particulate in a fluid flow

ABSTRACT

A method of facilitating removal of particulate from a fluid stream whereby individual particles of the particulate are agglomerated to form larger and therefore more easily removable particles. The particulate is passed through a zone which contains electric charging regions disposed at locations transversely spaced across the fluid stream and adapted to charge the particulate. Charge regions are alternately charged across the stream; that is, contiguous charge regions contain oppositely polarized electric fields, thereby to create transverse to the stream small regions where the particulate is charged positive, say, immediately adjacent to regions where it is charged negative. The thusly charged particles are then mixed to bring the oppositely charged particles into close proximity, one with the other, and small particles of the particulate agglomerate upon larger particles. The agglomerated particulate is then precipitated or otherwise removed from the fluid.

[ METHOD FOR INDUCING AGGLOMERATION OF PARTICULATE IN A FLUID FLOW 1{75] Inventors: James R. Melcher, Lexington;

Kenneth S. Snchar, Cambridge, both of Mass.

[73] Assignee: Massachusetts Institute of Technology, Cambridge, Mass.

22 Filed: Jan. 25, 1971 21 App1.No.: 109,615

1111 3,755,122 [451 Aug. 28, 1973 8/1922 Great Britain 55/139 9/1970Japan 55/139 57 I ABSTRACT A method of facilitating removal ofparticulate from a fluid stream whereby individual particles of theparticulate are agglomerated to form larger and therefore more easilyremovable particles. The particulate is passed through a zone whichcontains electric charging regions disposed at locations transverselyspaced across the fluid stream and adapted to charge the particulate.Charge regions are alternately charged across the stream; that is,contiguous charge regions'contain oppositely polarized electric. fields,thereby to create transverse to the stream small regions where theparticulate is charged positive, say, immediately adjacent to regionswhere it is charged negative. The thusly charged particles are thenmixed to bring the oppositely charged particles into close proximity,one with the other, and small particles of the particulate agglomerateupon larger particles. The agglomerated particulate is then precipitatedor otherwise removed from the 521 U.S. c1. 204/186, 55/107 [51] Int. Cl.B03c 5/00, C02b 1/78 [58] Field of Search 204/186-191, 302-308; 55/107,136-139,DIG. 25

[56] References Cited UNITED STATES PATENTS 3,496,701 '2/1970 Berg204/302 2,758,666 8/1956 Prentiss. 55/107 2,318,093 5/1943 Denney...204/317 FOREIGN PATENTS OR APPLICATIONS 846,522 8/1960 Great Britain.1 55/139 464,192 4/1937 Great Britain 55/139 SOURCE OF PARTICULATECHARGING ENTRAINED ZONE IN FLUID SOURCE OF 7 ELECTRIC POTENTIAL fluid.

5 Claims, 18 Drawing Figures MIXING 1 a AGGLOMERATING ZONE ZONEDISCHARGE PRECIPITATOR SCRUBBER,

SETTING,ETC.

PATENTEDmisza ms 7 sum 1 or 5 GGLOMERATING ZONE D S HARGE P R ECIPITATOR,

SCRUBBER, SETT|NG,ETC.

CHARGING ZONE ' SOURCE OF ELECTRIC POTENTIAL SOURCE OF PART! CLLATEENTRAINED IN FLUID FIG.

FIG. 2

ACHAZ m H m s m m w mam m wm 8 '8 "H .m8 2C0 4 1/ f /2 1 L \\E/ N u [1115 5 vv .JD/ E Y LX w U w m I; a H: I; ///F/ J l A 9 Pmmmmsmn 3.755; 122sum 3 0r 5 G 0 FIG. 7A .FIG. 7B

. L J O v v 7 O IOI - O v O D O 0 LL RA J 1 L 1 CHARGING MIXING IAGGLOMERATING 0 ZONE ZONE ZONE SINGLE STAGE FIG. 8

INVENI'ORS JAMES R. MELCHER KENNE H R. SAC-H R ATORNEY The presentinvention relates to precipitator apparatus wherein particulate in afluid flow is induced to agglomerate by virtue of electric forcesbetween particles carried by the fluid stream. 7

In a book entitled Industrial Electrostatic Precipitation by Harry J.White, published by Addison-Wesley Publishing Company, Inc., in 1963,the author discusses electrostatic precipitators for removal ofsuspended particulate from gases. It is noted in the book, and isdiscussed in detail hereinafter, that such precipitators do not removeparticulate below certain sizes. This holds true for other types ofparticle removers (e.g., centrifuges and scrubbers), as well.Accordingly a principal object of the presentinvention-is to providemeans for reducing the population of small particles by increasing theaverage size of particulate in a fluid flow.

A further object is to provide a method and a means for effectingelectrical attraction between the individual particles of theparticulate in the fluid, thereby to cause them to unite to form largerparticles.

A still further object is to provide'amethod and means for creating azone in the fluid stream wherein there are positively chargedparticles-mingled orintermixed with negatively charged particles, toallow agglomeration of small particles of the particulate upon largerparticles thereof.

These and other objects are evident in'the following.

description of the invention and are particularly delineated in theappended claims.

The objects of the invention are attained by a method of electricallyinducing agglomeration of particulate in a fluid flow thatcomprisescharging adjacent transversely spaced regions, in a patternalternately positive and negative, thereby to'chargeparticles in suchadjacent regions respectively positive and negative. The particulate,once charged, moves out of the charging region, thereafter being mixedto cause oppositely charged particles to mingle sufficiently to provideelectric interaction therebetween. The electric'interaction agglomeratessmall particles of y the particulate upon larger particles thereof. Inthis way, the size'of the particles in the particulate is increased tofacilitate re-- moval thereof from the fluid and to make possibleremoval of the very small particles'which are notremovable at all usingmost commercial removal systems.-

The invention is discussed herein upon reference to the accompanyingdrawing, in which:

FIG. 6 is a modification of the electrode array shown in FIG. 2 andshows an electrode array or matrix 1 wherein short charging electrodesare oriented parallel FIG. 1 is a system diagram in block diagram form,

embodying the concepts of the present invention;

FIG. 2 is a partial sketch, partly cut away, and shows a portion of thesystem of FIG. I, particularly to illustrate in simplified formacharging zone wherein particles in a fluid flow are provided withpositive and negative electric charges, a mixing zone, and anagglomerating zone;

FIG. 3 is a view taken uponthe line 3-3 inFIG.-.2 looking in thedirection of the arrows;

FIG. 4 is a schematic circuit diagram ofa simple electric circuit foruse in connection withth'e chargingzone of FIG. 2;

FIG. 5 is a schematic representation of two of the charging electrodesshown in FIG. 2 to illustrate electric charge distribution about theelectrodes in the charging .zone;

to the fluid flow, rather than orthogonal thereto as shown in FIG. 2;

FIG. 7A shows the natural size distribution of particulate in a typicaldirty gas and FIG. 7B shows a more desirable distribution forparticulate removal purposes;

FIG. 8 shows, schematically, a single electrostatic agglomerating stageembodying the present inventive concept;

FIG. 9 shows a vortex sheet and charge distribution emanating from asingle wire electrode in the charging zone of FIG. 8, the wire beingdriven by a DC or a sinu-' soidal AC voltage;

FIG. 10 shows charge distribution at one instant for superposition ofvortices from several of the wires shown in FIG. 8; 1

FIGS. 11 A and 11B are discrete spectrum approximations usedto' breakintegral-differential equations into a system of coupled differentialequations representing families of particles of the particulate;

FIG. 12 is an agglomerating zone or section zone or section, perfonnancecharacterized by spatial distribution of two particles families injectedat x =0 in FIG. 8 with particle densities [ti (0), n,(0)] and'chargesper particle [1),(0), q (0)]and the'associated two-family distributionfunction;

FIG. 13 shows the effect of multi-staging the single underlyingprinciples involved in the present inventive concept, there follows inthe next few paragraphs a brief preliminary description of the apparatusinvolved, particular reference being made to FIGS. l6 of the drawing. Inthe discussion, the term particulate is used to define the overallcollection of material in a fluid flow, and particle is used to definethe individual elements of said material. The term fluid embraces bothgas and particular liquids; however, the largest part of the discussionrelates to gas, such as flu gases and the like.

Turning now to the drawing, apparatus isshown generally at 101 in FIG. 2for inducingagglomeration of particulate in a fluid flow. The apparatus101 includes a charging zone 2 that includes an array of electrodescomprising electrodes 5, 5', 5" and 5". A source of DC electricpotential 11 in FIG. 4 is connected to render the electrodes 5 and 5"positive, and a source of DC electric potential 12 is connected torender the electrodes ST and 5" negative. (As hereinafter discussed, thevoltage'sources 11 and 12 can be AC, in

which event the indicated polarities in FIG. 4 are mo-,

mentary in nature.) Thus, adjacent electrodes as, for example, theelectrodes 5 and 5', are connected to the potential source in suchfashion as to apply alternately positive and negative electricpotentialat any instant of time thereto; i.e., the electrodes 5 to 5"are alternately as the particles designated 10 of the particulate flowin the longitudinal or x direction in FIG. 2 past adjacent chargedregions (e.g., the positively charged region designated 14 and thenegatively charged region designated 15 around electrodes and 5.,respectively, in FIG. 5), the particles take on the charge of theparticular region through which each passes. As shown in FIG. 5, theparticles designated which have passed through the positive polarityregion 14 are positively charged, and the particles designated 10" whichpassed through the adjacent or contiguous, laterally displaced,

negative polarity region 15, are negatively charged;

The charged particles flow into a mixing zone 3 where, as laterexplained with particular reference to FIG. 10, they are mixed to causeoppositely charged particles 10 to mingle sufficiently to provideelectric interaction therebetween. The particles 10 then pass into anagglomerating zone 3, to allow precipitation of the small particles 10'in FIG. 5 upon the larger particles 10". In fact, the zones 3 and 4really are one drift zone in which, first, mixing predominates and thenagglomeration predominates. Following agglomeration, the particulate maybe precipitated by electrostatic precipitator means, by scrubbing, in acentrifuge, or bysome other means applicable to removing largeparticles, the alternate means being designated 6 in FIG. 1; and thefluid thereafter can be discharged. In FIG. 1 there is also shown asource of particulate, entrained in the fluid, and a source of electricpotential 7; the latter may be connected to an array of electrodes inthe manner before discussed. The electrodes 5, 5', etc. can be strung inthe y-direction shown in FIG. 3, to provide contiguous regions 14, 15,22, and 23, transversely spaced (i.e., in the z-direction), in which theelectric field spatially alternates from positive to negative potentialacross the space in the zdirection. The field may, however, betemporally alternating in a periodic fashion or static. The wires 55"'are secured to the inner walls of a conductive chamber or conduitdesignated 16 by insulators 9, 9', 9", and 9 on the left side andinsultors 8, 8', 8", and 8" on the right side, respectively, or thechamber 16 can itself be insulating. The adjacent electrodes may beshielded from one another by a shield 18 in FIG. 4, which is grounded atG. The electrodes may be oriented orthogonal to the fluid stream, asshown in FIG. 2, or they may be short electrodes oriented parallel tothe stream, as shown at 50, 50', 50", 50" and 50" in FIG. 6, the latterbeing laterally separated in the 2- y plane, again to provide areas ofalternate polarity at laterally separated regions, as shown. Turbulencemeans 3' may be provided.

There now follows a more detailed explanation of the invention. Smallparticles in a gas stream are typically the last to be removed from theflowing gas in a conventional precipitator. Among other factorscontributing to this phenomenon is the relatively low mobility of smallparticles. This can be illustrated by a simple but useful model in whichparticle precipitation to the walls of a tube or conduit havingcross-sectional area A and precipitating perimeter S is considered. Ifthere are n particles per unit volume of the particulate to becollected, and the electrically-induced radial velocity at theprecipitation wall is taken as w(the product of the particulate mobilityb and the radial electric field intensity at the wall), then in distancedx, there is a change in particle density dn given by the expression forsteady-state precipitation AUdn Swndx from Eq. (1) that the particledensity decays with distance at a rate typified by the decay length 1,,

1,, UA/Sw The smaller w, the greater the decay length I,,, and thereforethe greater the tube length required to achieve a given removal of theparticulate.

The particle conductivity is also a problem in a conventional device,because the charge precipitated with the particles on the walls fails toleak away if the particles are highly insulating. The resultingspace-chargeinduced contribution to the electric field tends to cancelthe volume field, and hence cut off the precipitation.

For purposes of discussion, suppose that a size distribution functionfor the particulate is defined by flT,a,t), where Tis the position inspace, a is the particle radius, and t is the time. The number densityof particles in the radius range a too 4140 at the position i and time tis:

fla) da particles/unit volume.

Typically, the particle distribution function might depend on size assketched in FIGS. 7A and 78. An object of the present invention is todescribe a device which tends to attenuate the particle population atlow radii by achieving attachment of the particles to larger ones.Hence, the distribution function is skewed toward the higher radii shownin FIG. 78 from the distribution in FIG. 7A.

Note that the decrease in numbers at low a could be dramatic withoutmuch of an increase in f at large radii: the attachment of a largenumber of small particles to a larger particle would result inrelatively little shift to the right in the larger particle range.

Particles themselves can be collection sites for smaller particles, muchas the precipitator electrodes.

are conventionally the collection sites. In such a device, the largerparticles are essential, hence must not be precipitated. By contrastwith the conventional precipitation approach, wherein the smallparticles are the last to be removed, here the smallest particles arereduced in population first. Hence, the device agglomerates smallparticles onto larger ones as a conditioning process, prior tofiltration by conventional techniques: electrostatic precipitators,cyclones, etc.

Fundamentally, the particle surfaces replace the collection electrodesurfaces, and a decay length analogous to that given by Eq. (2) could bedefined. lfthe collection particles (having radius R, number density N,and charge such that their surface electric field is 5,) are thought ofas being sites tantamount to removal of the particulate (having densityn and mobility b), then the particulate collected by a single collectingpar ticle per unit time is 4-u-RbE,n and NAdx times this quantity is thetotal particulate number collected in the 5. distance dx. Instead ofEq'. (I), the following expression obtains:

A test of the advantages inherent in using the particles as collectionsites rather than walls is made by comparing 1,, and I,,,. If E isdefined as the electric field at the wall of the conventionalprecipitator, then w =bE,,,, and the ratio of collection lengths is Thesurface-to-volume ratio of the conventional precipitator collectionchannel is S/A. Becuase 4'n-RN is the surface-to-volume ratio of thecollecting particles, it can be seen from Eq. (5) that any advantageobtained from using particles as collection sites comes from having ahigh relative surface-to-volume ratio. Note, however, that there is anadditional advantage if the collecting field E, can be made largecompared to that practical in a conventional precipitator collectionchannel.

Although the simple model resulting in Eq. (5) gives no clue as to howthe particles are to be used effectively as collection sites, it doesillustrate that a new type of scaling is introduced. The collection ofultra-small particles takes place in a region occupied by the system ofparticles; no electrodes are required. But to be efficient, a populationof collecting sites must be maintained. Large sized particles aredesirable, and should not be removed until after the small radii part ofthe particulate has been collected.

The mixture of large and small particles (the dirty gas) is shown inFIG. 8 entering the single stage or section 101 from the left. In thecharging zone 2 of the section 101, all sizes are charged in a mannerthat insures oppositely charged particles distributed throughout thesize range. This is done in one of two ways by means of corona sources:(a) the corona wires are driven by alternating voltage, so that theycharge particles in their vicinity positively and negatively as theystream by. The result is a traveling wave of charge immediatelyfollowing a given wire. The homogeneous system of charged particles isachieved by mixing in the zone 3 just downstream; wires are drivenalternately out of phase, so that mixing is augmented by cross-streamingof gas between regions downstream of neighboring charging wires; (b)wires are alternately maintained at positive and negative DC potentials.Thus, a stream of particles having the same sign of charge emanates froma given wire, but is mixed with the streams from the oppositely chargedneighbors as the gas passes through the mixing region.

Once the particles have become mixed and hence essentially neutralconditions are obtained at the macroscale the agglomeration processcaused by relative I motions of the particles at the microscale takesplace. For convenience, this process can be envisioned as occurring inthe agglomerating region 4 following the mixing region 3 shown in FIG.8. Actually, both mixing and agglomeration should occur in a distributedfashion throughout these regions. The mixing predominates at first, theagglomeration later. The regions are not distinguished by any electrodestructures, but rather are simply drift zones occupied by the flowingdirty gas.

6. It is this lack of components that makes the agglomerating mechanismproposed here an attractive one.

In the following paragraphs, design considerations are discussed foreach of the regimes shown in FIG. 8, so as to answer the importantquestions: How much charge per particle can be obtained in the chargingsection? What length of mixing region is required and how does thatdepend on the construction of the charging grid? and, What length ofagglomeration section is required to achieve a given clearance of smallparticles from the gas? The charging mechanism in the immediate vicinityof the charging electrodes is essentially of the conventional type. Asmentioned before, ions generated by corona discharge on the wires in thecharging zone 2 drift through the region (e.g., l4, 15, 22 and 23)traversed by the particles, and hence charge the particles, eitherdiffusively or by impact. The particles having sizes greater than about0.5 urn are charged by impact, while those that are smaller are chargedby diffusion.

In fact, other means of charging might be employed, and theagglomeration mechanism would still be effective. For example, thecollection particles could be liquid drops, and then an optional mode ofcharging would beto use charge induction as the particles are formed, orto use condensation on charge sites.

An estimate of the agglomerator performance requires the dependence ofparticle charge on particle radius, a. If it is assumed that theeffective charging field in the corona region is E,,, thenan impactcharging model leads to a charge-per-particle that saturates at thevalueq(a) 12 'rre aE,

Hence, with the assumption that E is set by the charging sectionarrangement and voltage, Eq. (6) gives the charge dependence on radiusat the inlet to the mixing region. Note that once the particles havebeen mixed, there is no macroscopic field. The effective collectionfield is that at the particle surface. For the charge given by Eq. (6),that field is simply Mien/ qfic 12 m o where F, signifies the positionof the charging saturation. In what follows, it is assumed that themixing zone 3 is crossed by the particles without decay of thissaturation charge, so that r', is the plane x 0 at the inlet of theagglomerating section. Any conglomeration in the mixing zone would tendto increase the effectiveness of the device. The following might beconsidered a worst-case analysis in that respect.

If the gas stream is operated at a large enough Reynolds' number (ReUd/v 50, where d is the wire diameter and v is the kinematic viscosityof the fluid), the alternately positive and negative vortices willtendto mix the fluid to a certain degree. In the case that the wire voltagesare driven sinusoidally at line frequency, the distance downstream overwhich the charge changes sign is considerably larger than'the scale ofeddies. For a 10 m/sec. flow, the former will be A =U/f 0.167 m, and fora wire with 10" m diameter, the latter will be on the order of a fewmillimeters. Thus, this mechanism alone will not produce a zero netcharge distribution.

Consider the fact, though, that the width of the wake increases inproportion to m where x is the downstreamdistance from a wire. That is,b/d 4 x/d where d is the wire diameter and b is the wake width. Thewakes from the two neighboring wires will intersect each other when x Fx, such that b D, with D the wire spacing. Since the voltages of theneighboring wires will be 180 out of phase, with either AC or DCexcitation, the mixing initiated at this point should tend to decreasethe net charge distribution. By the time that the flow reaches x lx,,,the mixing nears completion. That is, the flow approaches net chargeneutrality at a given point viewed on the scale of the most diluteparticles. Thus, for d m and D 10 :11 (see FIG. 10), the required mixinglength x,, is

The latter figure should be considered an upper bound on the mixinglength, since the flow is considered to be initially laminar whenincident on the wires. Typically, it would be turbulent before reachingthe charging zone 2. Other means to create turbulence and mixing may beused, as well.

As outlined above, the purpose of the agglomerating zone 4 is to achievean attentuation of the low particle size densities, as characterized bythe shift in distribution function fla) sketched in FIGS. 7A and 78.Hence, it is desirable to establish expressions that describe thedistribution of f( F,a,t). Because the charge per particle is alsovarying in the agglomerating process, a description of q(F,a,t) is alsorequired. To this end, there is stated below physical laws accountingfor the migration of particles and the conservation of their associatedcharges.

Thus, a means velocity for particles V, which for the present purposesis the gas velocity, is defined. Assume that the electrical forces havea negligible effect on the gas motion, so that V is a function of space'and time determined by the flow characteristics alone. More properly,when conservation of a certain size particle with a certain sign ofcharge is applied to a given volume, the effects of both turbulence andthe inter-particle electric fields average to zero. Taking this functionas known in describing the agglomerating zone, then conservation of thenumber of particles in a size range A is accounted for by 4 Here, SAa isthe number of particles per unit volume per second lost from Aa to othersize ranges, minus a similar number brought in by collection from othersize Actually, for each equation written for the positively chargedparticles of radius a, its twin expression can be written for itsoppositely charged counterpart. The particles changing the charge q ofEq. (9) are oppositely charged from it, and hence belong to the twinsystem. Assuming success in creating equal quantities of oppositelycharged particles of every size, then the particle distributions of eachsystem will be perfect images of each other.

In the following, the approximation is made that in any range ofinterest of the radii distribution, the number of particles leavingbecause of collection by larger particles greatly exceeds that comingin, because smaller particles have collected yet smaller particles, witha resulting increase in their size. Similar arguments pertain to theelectrical current carried by particles as they are collected. Thecurrent collected by a single particle of radius a, due to imageparticles in the size range M, is:

KM q( )fl A as, (m'. t) 4%.

Similarly, the number of particles/sec. collected by particles havingradius a from the range Aa(per unit volume) is Note that E, q(T,a',t)/41re,a' From Eq. (1 1), it follows that and from Eq. (10). thesingle-particle current due to all smaller impacting particles is:

1,(a )=J; K(a, a )da.

Thus, there is a pair of integral-differential equations governing f andq in the agglomerating section. These are obtained by inserting Eq. (12)and Eq. 11) into (8), to get:

Note that, in writing Eq. (14), it is assumed that the gas moves atsufficiently low velocities, relative to the speed of sound, to justifysetting 0. Also, all symbols used to represent charges are defined suchthat they are positive. Use is made of Eq. (14) to find the distributionfunction for the smaller particles, and to do so, the term on the rightcouples to the larger particles through their instantaneous chargedistribution. That distribution is brought in by Eq. (15) written forthe larger particles. The formulation is then complete, be-

cause the integral on the right in Eq. requires the particledistribution function for the smaller particles.

In view of the difficulties encountered in solving the coupledintegral-differential equations, Eqs. (14) and (15), it is convenient toapproximate the continuous distribution of radii by a discrete spectrumas shown in FIGS. 11A and 118. The continuous distribution isrepresented by breaking it into p discrete spectra, formally: 1

f(a) i nm u( m), (16) (16) for the density spectrum in the coagulationand,

charging equations, (14) and (15), providesasystem of coupleddifl'erential. equations Thus, a representation in terms of 2p nonlinearpartial differential equations is evolved.

' Of greatest practicalinterest is the steady-state condition. It, inaddition, the agglomerating geometryis essentially dependent on only theone spatial coordinate x, the system of Eqs. (17) and (18) reduces to dzGOU m=n+1 in my d qu b 7 dx at] $4} I p where U is the mean gas velocityin the xdirection.

To obtain both physical insight into the significance of the model andpreliminary quantitative assessments of the potential of the device, itis in order to consider the one-dimensional, steady-state systemcharacterized by Eqs. (19) and (20). The approa'ch also exhibits theessential nature of the particle interactions predicted by a p familyset of equations, if attention is limited to the interactions of twofamilies, a, and (1,, as sketched in FIG. 12.

For the present purposes, it is assumed that the mobilities of bothfamilies are representable in terms of a simple Stokes drag model II/ mwhere p. is the dynamic gas viscosity. Then, Eqs. (19) and.(20) reduceto the 2p 4 expressions t/ itmus/ mg 11 Notice that modeling of.thepresent system is again evident. The charge on the smaller particlesand'the number density of the larger ones is predicted by Eqs. (23and.(.24) to be constants: n,,= constant and-q, constam.

Equations (22) and (25) can then be combined and solved in terms of theinlet values a (0) and q, (0). It

is thenpossibleshow that Thattheseare solutions is evident by simplysubstituting Eqs. (26) and (27) into Eqs. (22 25).

A useful relation between the particle density n (x) and the charge perparticle q, (x) is obtained by observing from Eqs. (22) and (2S)thatl/n, dn ldx l/q dqJdx. Because n, and q, are constants, thisrelation can be integrated and the initial conditions used to show thatnan/aim) 0 E0 gag/r50) Thus, 1 is an essential design parameter.Assuming that all particles are charged to saturation by the sameeffective field E, in the charging section, then q, and q,(0) are givenrespectively by Eq. (6) and q, (0)Iq, aJ/a, Further, VJV,(n,a,')l(n,a,') where VJV is the ratio of total particle volumeconcentrations at the inlet to the section, and we can write the loadingparameter as 1; a /a V,/V l 5 This last expression makes it clear thatthe price paid for being able to completely collect the smallerparticles in a single section is a volume loading of V /V, a la If theparticles are to be effectively changed in radius by a factor of 10 in asingle stage, then the ratio of volume loadings of the large to thesmall particles must be in the same factor of 10. This statement usesthe fact that n 0 is the least value of the loading factor that gives adistribution of n (x) approaching zero as x In fact, for 1; 0, Eqs. (26)and (27) assume the simple forms Note that this expression does notdepend on the size a,. The following equation can be taken as a typical35 value:

This is a reasonable, typical length for a practical device.

There is a discussion in the paragraphs that follow of how feedback canbe used to further enhance the rapidity of agglomeration. That thelength 1* is of a significance similar to that illustrated in theintroduction by I, is seen by noting that b /613m If it is furtherrecognized from Coulombs law that 41rRE, q/,, it follows that l, in Eq.(4) can be written as l, p U/bNq. For the particular case 1 0, Nq an,q,(0) q n,(0), and hence I, e,,U/b,q,n(0), which is seen to beidentical to 1*. v

For optimal use of a given volume, it is likely that agglomeration isbest achieved by having several, or perhaps many, stages 101 in series.An index as to the necessity of using series staging is the loadingparameter 1 Clearly, if 1 is considerably less than zero, staging isrequired, or only fractional clearance of the small particulate will beachieved, no matter how long the agglomeration section, but, even if 1is on the order of zero, it may be desirable to use some form ofmultiple staging. (I

There follows a discussion of the manner in which the previousderivations give the performance of stages, as shown in FIG. 9, orseries, as shown in FIG. 13. There then follows a discussion of analternative or complementary approach in which feedback of particles isof series sections, feedback or both is a trade-off with loading and,ultimately, overall systems considerations will dictate whichcombination of equipment and loading should be used.

A series of s stages is shown in FIG. 13. Each stage consists basicallyof charging wires and a drift space for mixing and agglomeration, assketched in FIG. 8. Parameters for each stage are summarized with thefigure. It is assumed that each charging section renews thecharge/particle to the same value as that achieved at the inlet to thefirst stage. Thus, q,(0) is the same for each stage, but in general, theloading of n at the stage inlets varies, hence each stage has itsassociated loading parameter and characteristic decay length 1*. For thei stage, [from Eq. (26)]:

and hence the removal of particulate for the system as a whole is wherethe parameters are defined such that n, number density of particles nleaving ith stage,

I, length of ith stage,

q,(0) saturation charge per particle of q family entering anagglomeration zone,

"i [q=( =/q1m and t? 'M I o QI 'H Another way of increasing theefficiency of the system is to use the large and quite valuableparticles more than once in a given section. This is accomplished ifsome of the particles at the outlet of the total agglomerator section(perhaps itself consisting of a series of stages) are fed back to theinput as illustrated in FIG. 14. The feedback is illustrated for thetwo-family system, but the general approach which is outlined could beequally well applied, with some complication, to a larger number offamilies.

The relation between input and output number densities n," and n,' isrequired. A fraction )0 l of the jth spectrum is separated and fed backto the inlet of the agglomerator (0 x, l). The general problem iscomplex, because the relationship between n, and n,

for a given family depends on the resident number denfrom which itfollows that n, n,"', but more important, that:

Thus, the large particle number density in the agglomerator is enhanced.

Now, a gain G 1 for the agglomerator section is defined such that andthe effect of feeding back the large particles is to increase 1; andhence increase G as'computedfrom Eq. (41 But, in addition, a fraction ofthe small particles is fed back. This fraction might bemost-conveniently selected as equal to that for the large particles. Inany case, feedback relations forthe small particles are, in addition toEq. (40):

"i "i xim' and it follows that the output number density'is related tothe input density by Thus, the feedback accomplishes an improvement inthe efficiency of particle agglomeration by subjecting the smallparticles to more than one pass through the agglomerator, as reflectedby Eq. (44), andalso improving the effect of the agglomerator inattenuating the small particles because of the residence ,of alargernumber of large particles [Eq. (41) with '1; computed using n,= n, fromEq. (39)].

To estimate the effectiveness of such a device inan industrialapplication, it is in order to examine a onestage device which operateson the fly ash produced by burning pulverized coal in an electric powerstation. The size distribution in such a flow is given in FlG 15A.Notice that all sizes from less than 1 to greater than 100p. arerepresented in order'to transformthe distribution to make it compatiblewith the two-family analysis, the following identification is made. Theparticulate mass distributed between a 0 and a 1 1. is redefined as thesmall particle density m centered at a, 0.5 1.. The remaining mass,which in this case represents 99 percent of the total, is defined as thelarge particle mass density, with an effective radius of 10".. Thisredefined distribution is shown in FIG. 158..

For a typical total particulate loading of M 7 X 10" kg/m, that partattributed to the small particles is: M 7 X 10" kg/m. The loading factorin this case is:

X l0/10 (7 X 10 /7 X 10) '1 4 The spacing factor 01,, (see paragraphbefore Eq. 32) can be determined from the following relation Using theresults of Eqs. (26 and 27 we can determinethedensity andchargedistributions down the channel:

To achieve a removal efficiency of 99.9 percent for the smallparticulate, ie., have n,(x)/n,(0) 0.001, requires that theagglomeration region be at least 8. 9m in length. Because only a singlestage is required, this is a feasible length for a practical device.

The above, conclusion pertains to operation of just one stage. Supposethat two stages :are cascaded, each a meter in length. The output smallparticle concentration is given by Eqs. (34) and (35) for s 2 and I I l:a

Notice that, in cases like this where 1; 1, the effect of adding morestages rather than just extending the length of the first, is notparticularly significant.

To make it possible to meet specifications with a shorter length of asingle-stage system, part of the large exiting particles can be fed backto the input. Thus, let x, 0.9"and x, 0. From Eq. (39),

duction in the required length of the system and, again,

indicates practical device dimensions.

In passing, it should be pointed out that, even though there is anincrease in the large-particle concentration by a factor of ten, theyare still fairly well dispersed. Feedback has reduced a, from 52 to 24.

In the foregoing, it is assumed that the incoming stream contains asufficient number of large particles. If this is not the case, then somesuch large particles are introduced at the entrance, artificially.However, most industrial particulate flows contain sizes covering arather substantial range. For example, fly ash from pulverized coalcontains one percent by mass of submicron sized particles, and a full 50percent by mass of particulate larger then microns. Even if thisconcentration, n,, occurring naturally in the stream is not as large asdesired for a direct-coupled device, the feedback mechanism analyzedjust before will allow an increase by a factor of Ill-1; of theeffective large particulate concentration.

As alluded to in the last paragraph, most gas flows contain adistribution of radii, rather than contributions from just two widelyseparated ranges. To predict the alteration of the particledistribution, the full integraldifferential equations should be used.However, a reasonable picture of the nature of the operation can begeneralized from the two-particle case. The smaller particles will tendto attach themselves to the larger ones. The extent of this process canbe increased by increasing the large particle concentrations and theircharges, using them repeatedly, or even introducing large particles by aseeding process, or lengthening the effective agglomeration section. Inany case, it is evident that output distribution will be a skewedversion of the input one. The extent of the distortion will be inproportion to the system properties mentioned above.

Before concluding, it should be pointed out that this system also doesmuch to alleviate the problem caused by high resistivity material. Inordinary electrostatic devices, the dust can accumulate on the sidewalls to such an extent that the corona may be turned off. Thearrangement'disclosed herein has no such walls. In addition, thereintrainment problem which causes inefficiency in other devices isactively sought here. The turbulent flow tends to keep the corona wiresclear of resistive buildup, preventing shutdown and loss of many of thelarge, and quite valuable, particles.

The output of the cross-spectrum agglomerator can be fed into aconventional precipitating device. This might be an electrostaticprecipitator, a scrubber, a cyclone, a settling chamber, etc. It isrequired that such a device be just about 100 percent efficient inremoving the larger sized particulate. Since these may be on the orderof 10 to 100;; or larger, this task is certainly within the abilities ofdevices currently available.

In the foregoing description, and as previously mentioned, thediscussion is primarily relevant to a system wherein the fluid is a gas;however, the fluid may be a liquid such as, for example, hydrocarbonfuels, which are an example of relatively insulating liquids and theparticulate can be solids, liquids, or even biological particles. Also,as should be quite evident from the discussion, the terms transverselyand laterally apply to both the z-and the y-directions in the drawingand the charged regions are spaced transversely or laterally, one fromthe other, adjacent regions being oppositely polarized; that is, if oneelectrode is charged with a positive polarity, all the electrodesadjacent to that electrode are charged with a negative polarity toprovide contiguous regions of positive or negative polarity as beforediscussed (e.g., see the electrode 50 in FIG. 6). Of course, eachcharging electrode can be made in any specific region, as is known, of aplurality of individual electrodes, all bearing, at one instant of time,the same polarity. The foregoing technical description emphasizesagglomeration wherein smaller particles attach themselves to largerparticles; however, the mechanism holds true for agglomeration betweenparticles in the same size range as well.

Modification of the invention herein described will occur to personsskilled in the art, and all such modifications are deemed to be withinthe spirit and scope of the invention.

What is claimed is:

l.-A method of electrically inducing agglomeration of particulate in afluid flow, that comprises, charging particles of the particulate insome regions of the fluid positive and charging other particles in otherregions in the fluid negative, mixing the charged particles to causeoppositely charged particles to mingle sufficiently to provide electricinteraction therebetween, and agglom crating particles'of theparticulate upon other particles thereof, and feeding back at least someof the agglomerated particles into the fluid flow for subsequentagglomeration with smaller particles therein.

2. A method as set forth in claim 1 wherein a portion of the fluidcontaining the last mentioned agglomerated particles is fed back intothe fluid flow for said subsequent agglomeration.

3. A method as claimed in claim 1 in which the mixing is enhanced bytemporally alternating polarity of the charge regions thereby to achievea homogeneous system of charged particles, through cross-streaming ofthe fluid.

4. A method as claimed in claim 1 in which the regions are alternatelymaintained at positive and negative DC potentials to enhance saidmixing, by crossstreaming of the fluid and thereby achieve a homogeneoussystem of charged particles.

5. A method as claimed in claim 1 in which mixing is enhanced bycreating turbulence in the fluid thereby to achieve a homogeneous systemof charged particles.

t fi

2. A method as set forth in claim 1 wherein a portion of the fluidcontaining the last mentioned agglomerated particles is fed back intothe fluid flow for said subsequent agglomeration.
 3. A method as claimedin claim 1 in which the mixing is enhanced by temporally alternatingpolarity of the charge regions thereby to achieve a homogeneous systemof charged particles, through cross-streaming of the fluid.
 4. A methodas claimed in claim 1 in which the regions are alternately maintained atpositive and negative DC potentials to enhance said mixing bycross-streaming of the fluid and thereby achieve a homogeneous system ofcharged particles.
 5. A method as claimed in claim 1 in which mixing isenhanced by creating turbulence in the fluid thereby to achieve ahomogeneous system of charged particles.